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Numerous routing algorithms have been proposed for routing efficiently in mobile ad hoc networks (MANETs) embedded in two dimensional (2D) spaces. But, in practice, such networks are frequently arranged in three dimensional (3D) spaces where the assumptions made in two dimensions, such as the ability to extract a planar subgraph, break down. Recently, a new category of 3D position-based routing algorithms based on projecting the 3D MANET to a projection plane has been proposed. In particular, the adaptive least-squares projective (ALSP) face routing algorithm (Kao et al., 2007) achieves nearly guaranteed delivery but usually discovers excessively long routes to the destination. Referencing the idea of hybrid greedy-face-greedy (GFG) routing in 2D MANETs, we propose a local hybrid algorithm combining greedy routing with ALSP Face routing on projection planes. We show experimentally that this hybrid ALSP GFG routing algorithm on static 3D ad hoc networks can achieve nearly guaranteed delivery while discovering routes significantly closer in length to shortest paths. The mobility of nodes is handled by introducing the concepts of active sole nodes and a limited form of flooding called residual path finding to the ALSP GFG routing algorithm. Under mobility simulations, we demonstrate that the mobility-adapted hybrid routing algorithm can maintain high delivery rates with decreases in the average lengths of the paths discovered compared to shortest paths, without generating a large amount of flooding traffic.